The Laws of Evidence are not uniform across domestic Courts let alone internationally. Which court is your case being heard in? From your post, it sounds like it may be an administrative tribunal of some description.
An expert witness is just that, an expert. Regardless of whether the expert has been hired by your legal team, they will offer their opinion based on what they consider relevant to the facts within the brief. You are paying for their time, not for their opinion and therefore, unlike TV, an expert witness cannot be coerced into barracking for your side or argument. Although, it would be unusual for an expert to be hired unless there was a point to be scored for your own side.
As you've said the case has already failed on the evidence tabled/heard during the hearing, there's not much that can be done. However, if and only if (and it does not sound like this is the case) the expert concedes there was a mistake or ommission in their original report, you would most probably be at liberty to file an appeal within the mandated time for the case. This is the likely scenario in Australia anyway. I have only practiced international law in the US and am unfamiliar with domestic legislation.
You do seem to have lost trust in your EW. Delays are inevitable always but to represent your EW as telling 'lies' is a serious matter and shows a complete erosion of confidence in her/him. As such, I agree with your EW that it would be best if you found a new EW that you do trust and whom you feel is impartial. It is unlilely that this one can remain so if there has been conflict between you.
Why is it that you're speaking with the EW directly? Are you self represented? Why are you and the respondent coming to conclusions together? The respondent is on the other side and you should only be speaking to them via your solcitor or barrister. Is this a Family Law matter?
I believe LearnedHand is an attorney practicing in the US and your best bet would be to PM him. Hope this helps.